The so-called Ponzi scheme refers to the fact that the dealer promises a high interest rate to the deceived person, but in fact there is no value-added project, purely using the investment money of the latecomer to pay the interest of the previous victim. Pen "Fun" Pavilion www.biquge.info

For example, one trader claims to give investors a 10% return in 1 month. The first victim invested 1 million, and the maker did not invest in any project. By the next month, he would take $100,000 from the money paid by the new investors the following month and give it to the first investor.

The first investor receives interest purely from the investment money of other new investors, but the first investor does receive interest and tends to believe in the authenticity of the investment. After months of receiving the promised high interest, the victim began to call on his friends to join the ranks of such "fortunes". In this way, the Ponzi scheme was able to survive.

Of course, we know that without a real value program to back it up, such a scam will eventually come to an end.

So how to identify an investment project, whether it is a Ponzi scheme?

In fact, the most obvious feature is the abnormally high interest rate.

Maybe you think that 10% interest a month is not too high, let me tell you a little story.

Legend has it that the king was so pleased with the invention of chess that he decided to reward Sita with a reward, and Sita said, "I don't want your reward, but your majesty, just give me some wheat on my board." Put 1 grain in the 1st slot of the board, 2 in the 2nd slot, 4 in the 3rd slot, 8 in the 4th slot, and so on, until the number of grains in each cell is twice as many as in the previous grid, until the 64th cell is full." A few decimals, a few grains of wheat, why is it so difficult, "come", the king has the full amount paid to Sita.?

The work of counting the wheat grains begins, placing 1 grain in the first compartment, 2 grains in the second compartment, and 2' grains in the third compartment,... Before the twentieth square was reached, the sack of wheat was empty. Sacks and sacks of wheat were carried before the king. However, the number of grains of wheat increased rapidly, and the king soon saw that even if he took out the grain of the whole country, he would not be able to keep his promise to Sita.

It turns out that the total number of wheat grains required is: =18446744073709551615?

How much wheat is there? about 82 billion tons. According to the current global barley production, it will take about 550 years to meet this is the miracle brought by compound interest, Einstein once exclaimed: "Compound interest is the greatest invention of mankind, the most powerful force in the universe, and the eighth wonder of the world." ”

You may think that a monthly return of 10% is not high, look at the chart below

That's why if there is a 10% rate of return, the rate at which wealth grows will eventually be a hit. If the 10% monthly return is real, then the next year, the 24th compound, will be 9.8, which is close to 10x.

And just another half a year, by the 30th month, it was 17.44 times. At the end of 3 years, it is 31 times.

If you invest 1 million, you should be rewarded with 31 million after 3 years.

If you plan to leave an inheritance to your children and grandchildren, a monthly rate of return of 10%, and give it to your children who have just started working for 20 years, so that they don't have to work hard to do jobs they don't like for money, and they can freely choose their careers.

If you invest $10,000 now, 240 months later, you'll have a return of 8.6 billion times, or 86 trillion in wealth, which is equivalent to the total GDP of the United States last year. You've only invested 10,000 yuan!

Speaking of which, you should understand that an investment opportunity with a 10% monthly return will not actively come to you.

There is indeed an investment opportunity in the world with a monthly return of 10%, but there will be a cap on the capacity because the market has a shock cost. In other words, if there are more people using the same strategy, the assets that the strategy needs to buy will fluctuate in price at the same time, so that they can no longer be purchased at the price required by the strategy.

For Wall Street hedge funds, an annualized return of more than 20% is enough to make a difference. Because for the local tyrants, the rate of appreciation of a large amount of property will only get slower and slower, and 20% is already a flying speed.

Speaking of which, it's already clear. If someone promises you 10% or more per month, you should know what's going on.

Again, I would like to warn you again: there will be no pie in the sky.

The characteristics of a Ponzi scheme are so obvious, but tried and tested. There is no doubt that the Ponzi scheme will end, but what interests me is when the Ponzi scheme will reach its climax and when will it be broken.

In the past two days, I have seen the papers of Nobel laureate Professor Robert Schiller in his early years, and he accurately predicted the inevitability of stock market crashes before many stock market crashes. The Ponzi scheme is used as an analogy to the stock market.

It seems that the study of Pond schemes not only has the effect of debunking the fraud, but can also be applied to the study of financial and securities speculation.

In his writings, Soros proposed a model of "reflexivity" to subvert traditional economic explanations. Professor Robert Shiller, on the other hand, uses a behavioral perspective to point out the shortcomings of traditional economic models.

The model presented by Soros presents two deviant views.

The price of a stock does not fluctuate around the value of the stock, but is "reflexive". That is, the increase in the price in the past brings about the expectation of appreciation, so new investors will buy and hold.

Rather than buying in favor of earnings per share, buy in the expectation that the share price will continue to rise and can be sold to later investors.

While there is room for the value of stocks to appreciate, what speculators expect here is about the same as a Ponzi scheme. That is, the benefits I expected were given by later joiners.

All of them are looking forward to future joiners, but the maximum number of participants, or the maximum amount of money for participants, is not infinite.

As a result, the whole process inevitably faces the same consequence as the Ponzi scheme - the bursting of the bubble.

The difference is that stocks are valuable after all, and there is nothing of real value behind a general Ponzi scheme. In other words, when the stock price goes all the way down, there will be a positive feedback effect, and later short sellers will expect the price to be lower, so they will sell more. Speculators in the early stages will have a situation similar to that in a stampede.

Once the stock price falls to the point where just holding the stock and getting dividends is also a good investment. Arbitrageurs will emerge, or we can call them "value investors". Just holding these cheap stocks and earning dividends can get a good rate of return.

This is the first deviant view that does not revolve around simple fluctuations in value, and that the investor's own behavior itself is a factor that will affect future prices.

The second deviant view is that when the price is pushed up by speculators, the listed company's ability to raise funds will increase, leading to an increase in its original value. More people buy stocks, and the company's ability to raise funds will help it expand its business.

When it falls, there will be a similar phenomenon of a bank run. A company with good fundamentals can suffer losses due to a tragic share price decline, causing the company's value to suffer.

The observer itself influences what is observed, and the observer of the classical model has nothing to do with it.

Let's define a generalized Ponzi scheme here: speculators want to generate returns from the speculators' new capital later on, rather than being optimistic about the value of the asset itself.

After a brief search, I didn't find a good mathematical model of the Ponzi scheme, because of interest (idle), I briefly engaged in it with two colleagues.

The per-deposit function of a Ponzi scheme is defined as I(n)

n is the number of participations

The O(n) function is the function of withdrawal, and the ratio of the amount of withdrawal to the deposit is called the withdrawal intention of the month, which is expressed by the function P(n).

Withdrawals, on the other hand, contain principal and interest, and the rate of return is set to a fixed r

then the cash flow of the player in the current month N(n)=I(n)-O(n)

N(n)=I(n)-O(n)=I(n)-[P(n)*N(n-1)+N(n-1)*r]

It's a recursive formula. The problem is that we don't have access to the data on deposits and the willingness to withdraw funds. And the ledger of the Ponzi scheme maker is not available. (Whoever has operated the Ponzi scheme can quietly give me a ledger, I promise not to report you :P)

Helpless, I have to simulate it. Looking back at the process of the Ponzi scheme, it is all strikingly similar. Investors will be very cautious at first and try it small. When the experiment is successful three times, it will become crazy.

With the help of leverage is an unstoppable thing. But there is a limit to how much leverage can be used by everyone. So we used the normal distribution as a hypothesis to make a simulation.

symsx; f1=exp(-((x-10)/5)^2); s1=int(f1，x); s1=******(s1)

The meaning of this curve is that the initial deposit is relatively slow, and after about 5 successful practices, the deposit will grow rapidly, and then reach the maximum leverage and begin to converge.

The willingness to withdraw is also related to the financing ability, and the willingness to withdraw is relatively strong at the beginning of the attempt. After trying the Ponzi scheme for the first time, you will be asked to withdraw money to see if you have actually made money.

After a successful attempt many times, it will ask for a rollover of interest, and will not ask for a quick withdrawal until the ability to raise funds reaches the upper limit. Forced to increase the willingness to withdraw.

This is because a portion of the profits must be paid to the source of the financing.

P=(x-10)^2/500; er

The above chart is the curve of the willingness to withdraw, and it is about the 10th time in practice, and it is not willing to withdraw.

Finally, we use N(n) to simulate the cash inflow of the trader each month, which is a recursive function, and each time depends on the previous deposit and the victim's own situation.

O(1)=0;?

I(1)=(5*pi^(1/2)*erf(1/5-2))/2+5;?

N(1)=I(1); P(1)=(1-10)^2/500;

fori=2:40

?? MO=((5*pi^(1/2)*erf((i-1)/5-2))/2+5-O(1))*(0.1+(i-1-10)^2/500);

??? O(i)=MO;

??? I(i)=(5*pi^(1/2)*erf(i/5-2))/2+5;

??? P(i)=(i-10)^2/500;?

??? N(i)=I(i)+(0.9+P(i-1))*(I(i-1)-O(i-1));

?end

The above chart is the net income of the players each time, and the net income of the Ponzi scheme at the beginning of the short-term decline (basically all new entrants, so there will be a lot of small attempts), and then there will be a rapid growth.

We set a 10% return per return, and the withdrawal willingness and deposit speed are all simulated, without any basis, and are completely in line with my intuitive feelings.

The implementation of such a model hits an inflection point around the 18th time, when the player can feel that the rate of revenue growth is zero. The pressure on withdrawals began to increase sharply. (By the way, 18 months after the start of the bonus mode, the Iron Exchange began to increase 100% of the funds, and the intensity was increased insanely.) The arbitrage return is about 10% each time, and the results simulated by our assumptions are very consistent. Considering that IronFX has a large amount of marketing costs, the financial pressure should be earlier than the 18th month)

This is followed by a compound interest increase in the interest commitment, which reduces the rate of increase in the maker's income sharply. When the practice reaches around the 36th to 37th time, negative growth begins, that is, the player of the month is not profitable.

In fact, players don't have to wait until it turns into a loss-making business to leave. When the time reaches about 18 times, you can start to clean up, and it will take some time to transfer the funds. Then by about the 31st or 32nd time, it was almost done.

As you can see, the model of the Ponzi scheme is asymmetrical. The rate of rise is not as fast as the rate of falling, and it will fall below the initial value.

Such a kind of continuous iteration and recursion, without the support of intrinsic value, such as a pure Ponzi scheme, is a worthless thing.

This chart is very interesting, let's take a look at the model of asset prices given by Soros:

If Soros is right, asset price climbs are mutually influencing and a Ponzi scheme-like scenario of waiting for the next house to take over, then the bubble will fall significantly faster than it will rise.

The rise is a slow rise, while the fall is a sudden stock market crash. Behind it is the principle of compound interest model.

When the price of the asset has made the dividends generated by holding it very cost-effective compared to the stock price, then buying the asset will be a similar arbitrage opportunity.

Even if the asset falls to near 0, there is no need to be afraid.

And as long as this happens, it will be a once-in-a-lifetime opportunity for dividend-oriented investors. And once such an opportunity arises a few times, we can use the magic of compound interest again.

As long as there are a few stock market crashes, compound interest will propel us to the position of the world's richest man.

This time the compound interest model really happened to be powerful, and I think everyone should think of the same person.

This bottom-buying strategy does not need to consider when the Ponzi scheme will collapse, what is needed is a strong estimation ability, knowing whether the assets bought at the current price can be ignored in the future.

I'm more concerned about when the Ponzi scheme, the model that relies on newcomers to pay interest to old players, will collapse and whether there is any precursor.

Since there is an upper limit to leverage, and the upper limit of leverage leads to an increase in our willingness to withdraw, and the growth of the function P(n) causes a crash, then there are at least two cases:

(1) The financing capacity reaches the upper limit, and it is impossible to borrow more money to maintain it. Then, just look at the participants' financing leverage to know that the inflection point will come.

(2) The leverage ratio is forced to be reduced, and if the central bank raises interest rates and other factors cause a sudden change in the financing situation, the inflection point will come suddenly.

This explanation of why central bank tightening is often preceded by stock market crashes may be self-justifying.

Of course, this is just a small model that is casually simulated on a whim today. It is impossible to really explain the mysterious market behavior, nor can it be taken seriously as a model for asset price prediction.

We just need to remember that the "good opportunity" of investing much higher than the normal interest rate will be a big hole.

As long as you can guarantee that you will not covet abnormally high interest rates, any Ponzi scheme will be helpless against you.

Author: Xu Zhe